Dynamical Quantum Algorithms For Chemistry and Materials

We present a series of dynamical quantum computing algorithms for use in quantum chemistry and materials. With application to a range of time and frequency dependent problems, and also eigenvalue decompositions. We show how dynamical algorithms are naturally well suited to quantum computers and may be a promising route to quantum advantage. 

One example we present is the Jaynes Cumming model for fermion-boson dynamics using the Holstein Primakov qubit mapping transformation to the Pauli spin operators, which has application to nuclear-electron dynamics in molecules.

Another important application of dynamical algorithms are Green’s functions. We demonstrate quantum algorithms for Green’s functions within the EUMEN quantum chemistry and materials package. Furthermore we use these quantum algorithms for Green’s functions in quantum embedding methods such as Dynamical Mean Field Theory (DMFT).

Finally, we present a low depth formulation of the recently developed Variational Phase Estimation (VPE) method, which can be thought of as a generalized eigenvalue decomposition in a time evolved basis. We therefore aim to show that time dependant algorithms are a powerful subroutine in near and intermediate scale quantum algorithms for quantum chemistry and materials.